NDT Advance Access originally published online on December 8, 2007
Nephrology Dialysis Transplantation 2008 23(5):1650-1658; doi:10.1093/ndt/gfm849
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Third-generation parathyroid hormone assays and all-cause mortality in incident dialysis patients: the CHOICE study
1 Departments of Medicine and Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY 2 Department of Medicine, The Johns Hopkins University School of Medicine 3 Welch Center for Prevention, Epidemiology and Clinical Research, The Johns Hopkins University 4 Cork University Hospital, Cork, Ireland 5 The Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 6 Scantibodies Laboratory, Santee, CA, USA
Correspondence and offprint requests to: Michal L. Melamed, 1300 Morris Park Avenue, Ullmann 615, Bronx, NY 10461, USA. Tel: 718-430-2304; Fax: 718-430-8963; E-mail: mmelamed{at}aecom.yu.edu
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Abstract |
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Background. There has been controversy about the utility of new third-generation parathyroid hormone (PTH) assays measuring only 1–84 PTH, with few large studies comparing second- and third-generation PTH measurements in patients with ESRD.
Methods. We measured 1–84 PTH (‘biointact’ or ‘whole’ PTH) and total PTH (‘intact’ PTH) in a national cohort of 515 incident dialysis patients from banked frozen EDTA plasma (median follow-up, 35 months) and examined the accuracy of estimating 1–84 PTH from total PTH and the associations of these levels with patient characteristics and mortality.
Results. The 1–84 PTH and total PTH levels were closely correlated. Higher 1–84 PTH was associated with African-American race and higher serum phosphate and lower calcium levels. The percentage of total PTH represented by 1–84 PTH was, on average, 53%, but with a wide range (25–89%). Calculating 1–84 PTH from total PTH using a proposed standard conversion factor (54%) led to misclassification of 8% of the population compared with measured 1–84 PTH. In a multivariate Cox proportional hazards model for all-cause mortality, a 1–84 PTH value >160 pg/ml was associated with increased risk of mortality (HR = 1.62, 95% CI, 1.03–2.54) compared to a level of 80–160 pg/ml. Elevated total PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio were not significantly associated with mortality.
Conclusions. The 1–84 PTH and total PTH are highly correlated. Elevated 1–84 PTH was significantly associated with increased mortality, whereas total PTH did not reach statistical significance. Thus, although in other respect they are similar, there may be utility in measuring 1–84 PTH for its associations with mortality.
Keywords: clinical epidemiology; hyperparathyroidism; mortality risk; parathyroid hormone; PTH assays
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Introduction |
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There are several currently available methods for measuring serum parathyroid hormone (PTH) levels [1]. The traditional second-generation assays of PTH, or intact PTH assays, which have been widely used in clinical practice, are now known to measure both the whole PTH molecule (1–84 amino acids) and other large PTH fragments, the most common of which is the 7–84 PTH fragment [2]. Recently, several third-generation PTH assays (a.k.a. whole or bioactive) that detect only 1–84 PTH have been developed [2], although it has been demonstrated that these assays do not generate the same results for the same ESRD patient specimens [3]. A new laboratory parameter was introduced along with the third-generation PTH assays, the ratio between 1–84 PTH and 7–84 PTH. These new assays are increasingly used in clinical practice, although clinical guidelines for targets in the dialysis population have not been established. In order to establish guidelines, studies are needed to evaluate these new assays with clinical outcomes.
Important clinical outcomes associated with secondary hyperparathyroidism in dialysis patients include, among others, the development of metabolic bone disease, assessed through bone histomorphometry, and both all-cause and cardiovascular-specific mortality. One third-generation PTH assay has been shown to have similar predictive value as second-generation PTH assays for bone disease assessed through bone biopsies in pediatric patients [4]. There have been conflicting data about the use of the 1–84 PTH/7–84 PTH ratio as a predictor of bone histomorphometry in adult patients [5–7] and, therefore, some controversy about the utility of the different methods of measuring PTH. To our knowledge, there have been no studies evaluating the associations of plasma PTH as measured by new assays or the 1–84 PTH/7–84 PTH ratio with mortality. In a large clinical trial of CinacalcetTM which did not assess clinical outcomes, Martin et al., using another third-generation PTH assay, showed that PTH can be monitored with either the second- or third-generation PTH assay [8]. He also suggested that a good estimation of 1–84 PTH is 54% of the total PTH value, and recommended values of 80–160 pg/ml as the equivalent KDOQI acceptable range for one of the newer third-generation PTH assays [8].
All-cause and cardiovascular specific mortality have been associated with secondary hyperparathyroidism [9,10], although not in all studies [11]. All previous studies showing an association between elevated PTH levels and mortality have used the second-generation PTH assays. We undertook this study to examine the clinical utility of one of the third-generation PTH assays in order to provide data pertinent to the controversy about PTH measurement methods. As such, our aims were three-fold: (1) to describe the clinical and laboratory characteristics associated with 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio, (2) to evaluate misclassification of 1–84 PTH status that results from taking a standard fixed percentage of total PTH as previously suggested [8], and (3) to evaluate the associations and independence of 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio with all-cause mortality.
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Subjects and methods |
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Study design and population
We conducted a national cohort study using a sub-cohort of the Choices for Healthy Outcomes in Caring for End-Stage Renal Disease (CHOICE) Study. CHOICE is a national, prospective cohort study investigating dialysis treatment choices and patient outcomes in incident end-stage renal disease (ESRD) patients. A total of 1041 dialysis patients (767 haemodialysis and 274 peritoneal dialysis) were enrolled in the USA from 81 dialysis clinics in 19 states between October 1995 and June 1998. These included clinics associated with Dialysis Clinic, Inc. (DCI, Nashville, TN, USA; n = 923), New Haven CAPD (New Haven, CT, USA; n = 86) and St Raphael's Hospital (New Haven, CT, USA; n = 32). Entry criteria included the initiation of chronic outpatient dialysis in the preceding 3 months, ability to provide informed consent for participation, age older than 17 years and ability to speak English or Spanish.
A specimen bank was established to store blood samples only from the DCI participants, and specimens were obtained for 898 (97.3%) of the DCI enrolees. The Johns Hopkins University School of Medicine Institutional Review Board and the review boards for the clinical centers approved the study protocol. All patients gave written informed consent before participation in the study.
Data collection
Blood used for PTH analysis was collected from the CHOICE study participants as part of a special lab specimen draw. Plasma from special draws was available for 773 patients (86% of the specimen bank participants) from 2 to 33 months after dialysis initiation, with 515 patients having plasma within 6 months of dialysis initiation. A lavender top tube (EDTA) was collected pre-dialysis, immediately centrifuged at 2500–3000 rpm for 15 min, separated and refrigerated. PTH has been shown to be stable for 72 h in refrigerated EDTA plasma [12]. Specimens were then mailed by overnight courier, divided into aliquots and then stored at –80°C until they were thawed for analysis at Scantibodies Clinical Laboratory (SCL; Santee, CA, USA) for PTH measurements.
PTH assays
To confirm the ability to recover parathyroid hormone from long term frozen specimens, we performed a pilot study in which we thawed and reran the original PTH assay (Diasorin IRMA) on special draw specimens from 10 patients who had had PTH assays performed for routine clinical care on the same day as the special lab draw for this study. The correlation coefficient between the original values and the long term frozen and thawed values was 0.97. These samples were also tested using Scantibodies total PTH assay, and the correlation coefficients with both the clinical care results and the Diasorin assay on thawed specimens were >0.97. SCL performed testing on 773 thawed samples for total PTH value [interassay coefficient of variation (CV), 6.7%] and 1–84 PTH value (CV 12.4%) and then the derived 7–84 PTH value (total PTH – 1–84 PTH) and the 1–84 PTH/7–84 PTH ratio were calculated from these values. Although several fragments compose the non-1–84 portion of total PTH, the term 7–84 PTH will be used to describe all these fragments. The specimens were shipped to SCL with unique numbers but no other patient-identifying information, thereby masking SCL from all patient information. Masked duplicate specimens were sent (n = 30) for quality control. The code for linking the subject with the test result was kept confidential at the CHOICE coordinating center. SCL had no role in the data analysis. Because PTH values change over the course of dialysis, it was decided to use only PTH values from within the first 6 months of dialysis initiation for this analysis, leaving a final sample of 515 dialysis patients.
Other laboratory measures
Other laboratory measures included 3-month average measures of serum calcium, phosphate, albumin and haemoglobin, from dates that were closest available to the special lab draw date. Serum calcium was adjusted for albumin using the formula: adjusted calcium = measured calcium – [(4.0 – serum albumin in g/dl) x 0.8]. All calcium values reported and used in this analysis were corrected using the above formula. High-sensitivity C-reactive protein (CRP) was measured from frozen serum from all patients with available serum in the specimen bank within a median of 5 months from the initiation of dialysis. CRP and PTH values were log-transformed in some analyses due to their non-normal distributions.
Medical history data
Data regarding patient demographics and medical history were collected from a self-report questionnaire and chart review. The patients’ first visit to a nephrologist was ascertained through a baseline questionnaire [13]. Race was self-categorized and coded as African American or white/other (including Hispanic, Asian and Native American). The degree of comorbidity severity was assessed using the Index of Coexistent Disease (ICED), an instrument that has been validated in dialysis populations [14]. The composite ICED score ranges from 0 to 3 (with 3 indicating highest severity), and is calculated from two constituent indices, the 19-axis Index of Disease Severity (IDS) and the 11-axis Index of Physical Impairment (IPI). Dialysis modality at baseline was defined as the modality at 4 weeks after enrolment in the study and was categorized as haemodialysis or peritoneal dialysis. Injectable vitamin D use data, available for calcitriol but no other vitamin D formulation, were obtained from linked United States Renal Data System billing data. Patients were categorized as having received or not received injectable vitamin D over follow-up. Mortality was ascertained through communication with the dialysis clinics, monthly reports from the central DCI database and using Centers for Medicare and Medicaid Services (CMS) and National Death Index data.
Statistical analysis
Distributions of 1–84 PTH, 7–84 PTH and the 1–84 PTH/ 7–84 PTH ratio were compared in patients according to age, race, sex, presence of diabetes mellitus, serum calcium and serum phosphate using the Wilcoxon rank-sum test. Separate linear regressions of 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio were performed with adjustment for age, race, sex, dialysis modality, smoking, diabetes mellitus, referral time, BMI, CRP, albumin, calcium and phosphate. Pearson's correlations with Bonferroni correction for P-values were performed between the different PTH measurements as well as the 1–84 PTH/7–84 PTH ratio. Correlations were examined visually using scatter plots. Diasorin IRMA PTH assay results and SCL total PTH assay results from blood drawn on the same day were compared using the Wilcoxon matched-pair signed-ranks test.
To test whether using 54% of the total PTH level provided acceptable estimates of the 1–84 PTH level, we calculated the 1–84 fraction using 54% of the total PTH. We then used modified KDOQI (National Kidney Foundation's Kidney Disease Outcome Quality Initiative for Bone and Mineral Metabolism Clinical Guidelines) cutoffs of 80–160 pg/ml (54% of KDOQI recommended 150–300 pg/ml) for 1– 84 PTH to assess misclassification and percent agreement. To assess the reliability of using the 54% conversion factor against total PTH values to estimate 1–84 PTH values, we further compared calculated 1–84 PTH to measured 1– 84 PTH values. Equivalence was defined as the calculated values being within 10% of the measured value. To assess the presence of any systematic bias in using 1–84 PTH as 54% of the total PTH we created Bland–Altman plots to examine the difference between the measurements (calculated 1–84 PTH – measured 1–84 PTH) against the mean of the measurements [(calculated 1–84 PTH + measured 1–84 PTH)/2]. To evaluate any changes in the percentage of total PTH represented by 1–84 PTH as total PTH increases, we plotted the 1–84 PTH% versus total PTH. We also averaged the 1–84 PTH% at different total PTH KDOQI guideline values.
We used Cox proportional hazards analysis to assess the presence, strength, independence and statistical significance of the association of different PTH measurements with all-cause mortality. In this analysis, PTH values were categorized based on current modified KDOQI guidelines and the 1–84 PTH/7–84 PTH ratio was categorized into tertiles. Using modified KDOQI guideline cutoffs was equivalent to using quintiles and combining the middle three quintile categories. Potential confounders included in the model were age, race, sex, baseline modality, smoking (ever/never), diabetes mellitus, ICED, referral time, employment, intravenous calcitriol use, BMI, log (CRP), albumin, haemoglobin, calcium and phosphate. Missing values for referral time were imputed using age, race, sex, education, ICED category, diabetes, haemoglobin and albumin as predictors. Analyses were also performed excluding those with missing referral times. Patients were censored at transplantation or last date of follow-up (31 December 2002). All analyses were stratified by clinic to account for possible inter-clinic clinical variability. The threshold for statistical significance was set at a two-sided P-value of <0.05. Statistical analyses were performed using Stata software, version 8.2 (Stata Corporation, College Station, TX, USA).
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Results |
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Characteristics of the study population
There were 515 patients in the CHOICE cohort who had serum available for testing within the first 6 months of initiation of dialysis [median 4.5 months from start of dialysis; intraquartile range (IQR), 3.9–5.2 months]. The characteristics of patients who had 1–84 PTH testing performed were similar to the overall DCI CHOICE cohort (Table 1). Patients were followed for a median 35 months (IQR 15–55 months).
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Distribution of 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio
The median 1–84 PTH value for the 515 patients was 53 pg/ml (IQR 22–134 pg/ml) (Table 2). African Americans and patients with low serum calcium and high serum phosphate had higher 1–84 PTH levels. The median 7–84 PTH value in the population was 54 pg/ml (IQR 21–109 pg/ml). Patients who were younger than 65 years, were African American, were on peritoneal dialysis and had lower serum calcium and higher serum phosphate had significantly higher median 7–84 PTH values. Patients who were older than 65 years, African American, on peritoneal dialysis, and had diabetes mellitus, serum calcium <9.0 mg/dl and serum phosphate <5.5 mg/dl had higher 1–84 PTH/7–84 PTH ratios (Table 2).
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Association of 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio with patient characteristics
In multivariate linear regression, patient characteristics associated with greater 1–84 PTH values include African-American race, male sex, having been referred to a nephrologist >4 months before initiating dialysis, and having higher BMI, lower serum calcium and higher serum phosphate (Table 3). Patient characteristics associated with greater 7–84 PTH values include African-American race, male sex, referral to a nephrologist >4 months before dialysis initiation, lower serum calcium and higher serum phosphate (Table 3). Patient characteristics associated with the greater 1–84 PTH/7–84 PTH ratio include increased age, higher BMI and lower serum phosphate levels (Table 3).
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Correlations among total PTH, Diasorin IRMA intact PTH, 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio
Total PTH, 1–84 PTH and 7–84 PTH were all highly correlated (
= 0.99, P < 0.001 for total PTH versus 1–84 PTH, = 0.93, P < 0.001 for 1–84 PTH versus 7–84 PTH, = 0.98, P < 0.001 for 7–84 PTH versus total PTH). The correlations between the 1–84 PTH/7–84 PTH ratio and total PTH, 1–84 PTH and 7–84 PTH were weaker ( = 0.08, P = 0.33 for 1–84 PTH/7–84 PTH ratio versus total PTH, = 0.18, P < 0.001 versus 1–84 PTH and = –0.03, P = 1.00 versus 7–84 PTH). There were 67 patients who had both Diasorin clinical care intact PTH assays and SCL total PTH testing performed on specimens drawn on the same day. The correlation coefficient between the two values in these patients was 0.94 (P < 0.001). The median (IQR) for the Diasorin intact PTH assay was 96 pg/ ml (35–176), whereas the median SCL total PTH was 124 pg/ml (47–249) (P = 0.002).
Measured versus calculated 1–84 PTH values
In the 515 patients with PTH measurements within 6 months of dialysis initiation the 1–84 PTH represented, on average, 53% of the total PTH, with a wide range (25- 89%). The 1–84 PTH percentage of total PTH (1–84 PTH%) increased as total PTH increased (Figure 1). At total PTH levels <150 pg/ml, the mean 1–84 PTH% was 51% (range, 25–85); at 150–300 pg/ml, the mean was 55% (range, 36–89) and at >300 pg/ml the mean was 57% (range, 32–73). When the 1–84 fraction was calculated using 54% of the intact PTH, 8% of the total population was misclassified into a different KDOQI category. The percent agreement was 92%. Stratified by KDOQI classifications, only 5% (16/308) of those below goal were misclassified, while 10% (10/96) and 12% (13/111) of those at or above goal, respectively, were misclassified. Only 41% of calculated PTH measurements were within 10% of the measured 1–84 PTH value. The Bland–Altman plot (Figure 2), showing the difference between the calculated and measured 1–84 PTH plotted against the mean of the two values, reveals that, at low 1–84 PTH levels, there is not a significant difference between the two values but that, as the 1–84 PTH levels increase, there is a large non-systematic difference between the two measures.
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Association of PTH assays with all-cause mortality
There were 239 deaths among the 455 patients (1346 person-years of follow-up) with complete data included in the survival analysis. In the final model, patients with higher levels of 1–84 PTH had a higher mortality compared to patients in the middle range of values (Table 4 and Figure 3). Having a 1–84 PTH >160 pg/ml was associated with a 62% increased risk of mortality. These associations were similar when models were run on the 455 patients with complete data and when those without referral time data (n = 73) were excluded from the analysis (data not shown). Successive models reveal negative confounding of the association between 1–84 PTH and mortality, with the risk increasing as additional covariates are added to the model. No single covariate changed the association more than the others. There was a trend toward a higher risk of death with elevated total PTH and 7–84 PTH but these associations were not statistically significant. There was a trend for lower mortality for 1–84 PTH/7–84 PTH ratios of 1.0–1.3, although this was also not statistically significant. Further adjustment for the 1–84 PTH/7–84 PTH ratio did not substantially modify the association of 1–84 PTH with mortality (data not shown). Additional adjustment for timing of blood draw since initiation of dialysis strengthened the association of 1–84 PTH with mortality (HR 1.67, 95% CI 1.06–2.63).
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Discussion |
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The first objective of this study was to characterize fully the relation between demographic and laboratory characteristics and 1–84 PTH, 7–84 PTH and their ratio in a large cohort of dialysis patients. In our population, patients with lower serum calcium had significantly higher levels of both 1–84 PTH and 7–84 PTH, and the 1–84 PTH/7–84 PTH ratio. While both 1–84 and 7–84 levels were elevated compared to patients with high serum calcium, the 1–84 levels were more elevated, leading to a difference in the ratio. This result is similar to that seen in previous studies [8]. Patients with higher serum phosphate in this study had significantly higher levels of 1–84 PTH and 7–84 PTH but lower levels of the 1–84 PTH/7–84 PTH ratio compared to patients with lower serum phosphate.
In linear regression analysis, the same factors that were associated with 1–84 PTH were also associated with 7–84 PTH, suggesting that there may be similar driving forces for both hormones. These included established parameters controlling PTH levels, including serum calcium, serum phosphate and race. Novel parameters associated with 1–84 PTH and 7–84 PTH found in this analysis include BMI, late referral time and sex.
The correlations between 1–84 PTH, 7–84 PTH and total PTH have been previously described [15] using PTH assays different from those used in this study. The Diasorin IRMA intact PTH assay averaged significantly lower than the SCL total PTH assay on blood drawn on the same day. The blood for the SCL total PTH assay was frozen for several years and then thawed for testing. Therefore, one may have suspected there to be some degradation of PTH, yet the measured PTH was found to be actually significantly higher. This indicates a difference in the actual assays, similar to recently published reports [16,17].
The second aim of this study was to evaluate the effect of using a standard percentage of total PTH as a surrogate for measuring 1–84 PTH itself. While many studies have reported the average percentage of total PTH represented by 1–84 PTH [7,8], we show that there is actually a wide variation in this number in this patient population. The percentage also appears to change as total PTH increases. Overall, using a calculated measure approximately 8% of all patients were misclassified, a number of unclear clinical significance. We also found that only 41% of calculated 1–84 PTH values were within 10% of the measured 1–84 PTH value. The Bland–Altman plot comparing calculated versus measured 1–84 PTH reveals that there is not a systematic bias in this comparison; thus, there is no simple correction formula enabling an accurate estimation for 1–84 PTH from total PTH. As current guidelines use total PTH values for treatment recommendation, the wide variation in 1–84 PTH may not matter currently. But as clinical practice and, with it, clinical evidence and guidelines shift toward the use of third-generation assays, this misclassification may become more important. The cutoffs of 80 pg/ml and 160 pg/ml for 1–84 PTH as suggested by Martin et al. [8] using a different third-generation PTH assay than the one used in this study need to be tested more rigorously.
To our knowledge, this is the first large study to test the associations of the third-generation PTH assay with mortality in a dialysis population. High levels of 1–84 PTH were associated with increased mortality, while elevated total PTH and 7–84 PTH were associated with higher point estimates as well, but not with statistical significance. The association between hyperparathyroidism and mortality has been found in other studies [9,10]. As in previous studies, the association with mortality was only found after adjustment for confounders [9]. Other studies examining PTH values in a time-dependent manner did not find a relationship [11]. In a previous analysis of the CHOICE study population, we found that baseline elevations of PTH, using the Diasorin IRMA assay, were not associated with mortality but that time-dependent values were [18]. In this analysis, we found that baseline elevated total PTH, using the Scantibodies assay, was not associated with mortality. This analysis differs from our previous study because the values are within 6 months of dialysis initiation rather than the 3 months around study enrolment.
There are several limitations to our study. The first is that we did not have data on the entire CHOICE cohort, which may have introduced an unmeasured selection bias, since only those who had the correct sample in the specimen bank were included. However, our final sample was similar to the overall DCI CHOICE sample. Another limitation is the use of a single PTH measurement. Because PTH values change over the course of dialysis, we only used PTH values within the first 6 months of initiation of dialysis but this did not account for PTH variability within individuals over the short term (i.e. day or week). Most previous studies have used single values of PTH to evaluate the association of mortality with secondary hyperparathyroidism [9]. Additionally, like all previous studies of these associations, this is an observational study and causality cannot be directly inferred. Our study examines the agreement between different measures of PTH and their association with mortality; we unfortunately cannot address the potential importance of the PTH ratio in the diagnosis and classification of renal osteodystrophy as bone biopsy data was not available for the study subjects.
In summary, in this national cohort of dialysis patients, 1–84 PTH, 7–84 PTH and total PTH were strongly correlated. There were significant differences in 1–84 PTH, 7–84 PTH and the 1–84 PTH/7–84 PTH ratio among different subgroups. These relationships need to be further clarified in larger and more heterogeneous populations of patients. Using a calculated measure of 1–84 PTH led to misclassification of 8% of patients and only 41% of calculated values were within 10% of measured values. Elevated 1–84 PTH was significantly associated with increased mortality in this population, whereas total PTH did not reach statistical significance, suggesting that there may be a clinical utility in measuring the 1–84 PTH independent of the total PTH. However, this finding should be taken with caution and viewed as preliminary because of the relatively statistically weak (P-value <0.05) association. Further research is needed in this area.
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Acknowledgments |
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This work was supported by grant no. R01DK59616 from the National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, MD, USA; grant no. R01HS08365 from the Agency for Health Care Research and Quality, Rockville, MD, USA; and grant no. R01HL62985 from the National Heart Lung and Blood Institute, Bethesda, MD, USA. M.L.M. is supported by grant F32DK069017 and K23DK078774, R.S.P. is supported by grant U01DK5730 and N.R.P. is supported by grant K24DK02643 from the National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, MD, USA. The authors thank the patients, staff and medical directors of the DCI clinics who contributed to the study. Some of the data reported here have been supplied by the United States Renal Data System (USRDS). The interpretation and reporting of these data are the responsibility of the authors and in no way should be seen as an official policy or interpretation of the US government.
Conflict of interest statement. Zan Yang and Tom Cantor are members of Scantibodies Laboratory and have a financial interest in the company. The other authors have no conflicts of interest to report. The results presented in this manuscript were presented, in part, at the 39th annual meeting of the American Society of Nephrology, San Diego, CA, USA, 2006. They have not been published elsewhere.
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Accepted in revised form: 4.11.07
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